LinearPowerSum

This is a Mathematica script to handle the linear power sums, i.e. the expressions of the form \sum_{i} c_i a_i^m in a symbolic way.

Usage

Load linearpowersum.m into Mathematica. Then, for example, the expression a*x^m+b*y^m can be represented as linPS[{a,b},{x,y},m]. It symbolically manipulates such expressions and related basic operations (such as scalar multiplication, addition, multiplication, and exponentiation). If you evaluate

linPS[{a, b}, {x, y}, m]^2

then it returns

linPS[{a^2, 2 a b, b^2}, {x^2, x y, y^2}, m]

Instead of m, you can put a linear polynomial in m with integer coefficients or an integer. For example,

2 linPS[{a, b}, {x, y}, 3 m - 1] + linPS[{c}, {z}, 2 m]

returns

linPS[{c, (2 a)/x, (2 b)/y}, {z^2, x^3, y^3}, m]

Similarly,

linPS[{a, b}, {x, y}, 3]

returns

a x^3 + b y^3

Sample script

Put the following two files in the same directory :

• linearpowersum.m : define linPS with its properties
• KR_character_G2.m (or KR_character_A1.m) : sample Mathematica script for the linear power sum expression of KR modules of type G2 (A1)

To run the sample script (assuming that the Mathematica kernel is on your path):

$ math -script KR_character_G2.m